Gauss decomposition for quantum groups and supergroups
From MaRDI portal
Publication:1375226
DOI10.1007/BF02364982zbMath0899.17002arXivq-alg/9505001MaRDI QIDQ1375226
M. A. Sokolov, E. V. Damaskinskiĭ, Petr P. Kulish
Publication date: 4 May 1998
Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/q-alg/9505001
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50)
Related Items
Lie superbialgebra structures on the Lie superalgebra C3+A and deformation of related integrable Hamiltonian systems ⋮ Universal T-matrix, representations of OSpq(1∕2) and little Q-Jacobi polynomials ⋮ Functional equations for transfer-matrix operators in open Hecke chain models ⋮ Gauss-Lusztig decomposition for positive quantum groups and representation by \(q\)-tori ⋮ Cayley–Hamilton theorem for quantum matrix algebras of $GL(m|n)$ type ⋮ Quantum matrix algebras of the \(\text{GL}(m|n)\) type: the structure and spectral parameterization of the characteristic subalgebra
Cites Work
- Unnamed Item
- Unnamed Item
- Central extensions of quantum current groups
- Computation of monodromy of certain W-invariant local systems of types B, C, D
- Quantum Berezinian and the classical Capelli identity
- Universal R-matrix of the quantum superalgebra osp(2\(| 1)\)
- Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras
- Quantum R-matrices and factorization problems
- A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
- \(q\)-oscillator realizations of the quantum superalgebras \(sl_ q(m,n)\) and \(osp_ q(m,2n)\)
- Quantum deformation of flag schemes and Grassmann schemes. I: A \(q\)- deformation of the shape-algebra for \(GL(n)\)
- Universal \(R\)-matrix for quantized (super)algebras
- An extension of the Borel-Weil construction to the quantum group \(U_ q(n)\)
- Quantum Lie superalgebras and q-oscillators
- Isomorphism of two realizations of quantum affine algebra \(U_ q(\widehat{\mathfrak{gl}}(n))\)
- Gauss decomposition of connection matrices and application to Yang-Baxter equation. I
- Quantum Lorentz group having Gauss decomposition property
- Yangians and Gelfand-Zetlin bases
- The dual of a quantum group
- On the bosonization of \(L\)-operators for the quantum affine algebra \(U_ q ({\mathfrak {sl}}_ 2)\)
- GENERALIZED GAUSS DECOMPOSITION OF TRIGONOMETRIC R-MATRICES
- THE SOq(N, R)-SYMMETRIC HARMONIC OSCILLATOR ON THE QUANTUM EUCLIDEAN SPACE ${\bf R}_q^N$ AND ITS HILBERT SPACE STRUCTURE
- Characteristic relations for quantum matrices
- Some aspects of quantum groups and supergroups
- On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q
- On the q oscillator and the quantum algebra suq(1,1)
- Generalized Gel’fand invariants and characteristic identities for quantum groups
- Differential geometry of the quantum supergroupGL q (1/1)
- Representations of quantum matrix algebra M q(2) and its q-boson realization
- Algebraic structures related to reflection equations
- Elementary operations and Laplace's theorem on quantum matrices
- Some remarks on the Gauss decomposition for quantum group GLq(n) with application to q-bosonization
- Boundary conditions for integrable quantum systems
- Duals of quasitriangular Hopf superalgebras and the classical limit
- Quantum groups SOq(N), Spq(n) have q-determinants, too
- Differential calculus on the quantum superspace and deformation of phase space
- Three-dimensional quantum groups from contractions of SU(2)q